I have asked girls out in just about any situation Imaginable. For the most part If you are not pushy, they don't mind. Even if their not interested they are usually flattered. One thing that I wouldn't advise however, is aproaching a stranger and just asking her for her number. You need to talk to them a little first. Like Katie said, don't walk up to a girl with a bunch of her friends when she is leaving a resturaunt and ask her for her name. I actually have done both of these things but I knew it was O.K. because of certain signs(looks, smiles,ect...). For the most part if you are just genuine and don't try to be something your not you are not going to bother her. I mean if a girl aproached you and was clearly interested in you and was sweet, but you weren't interested, Would that bother you? I know it is hard when anxeity gets in the way. But there really isn't any wrong place, theirs is just wrong times, and definatley wrong ways. If you have talked to a girl that you are interested in already, and she has smiled at you, there is nothing wrong with asking her for her number. You have more to gain than you have to lose.